# Aptitude - Square Root and Cube Root - Discussion

Discussion Forum : Square Root and Cube Root - General Questions (Q.No. 6)
6.

If a = 0.1039, then the value of 4a2 - 4a + 1 + 3a is:

0.1039
0.2078
1.1039
2.1039
Explanation:

4a2 - 4a + 1 + 3a = (1)2 + (2a)2 - 2 x 1 x 2a + 3a

= (1 - 2a)2 + 3a

= (1 - 2a) + 3a

= (1 + a)

= (1 + 0.1039)

= 1.1039

Discussion:
70 comments Page 1 of 7.

Nas said:   10 years ago
Guys let me explain this things.
Everyone discuss here is (a-b)^2.

Actually (a-b)^2= (b-a)^2.
For example (5-2)^2=(2-5)^2. Cause square of a negative no is positive.

But you guys know what's wrong in here. The wrong is square root of a no is either positive or negative. In solution taking square root come with +(1-2a) and -(1-2a) so while considering these two we get two answer.

Both of them will satisfy the condition. Hope you guys are get it. Here solution consider only one possibilities of answer.

Lokesh Ravella said:   9 years ago
4*a*a - 4*a + 1 can be written as 4*a*a - 2*a -2*a +1.
Taking 2*a common 2*a(2*a-1)-(2*a - 1).
Hence (2*a-1)(2*a-1).

4*a*a - 4*a + 1 can also be written as 1 + 4*a*a-4*a can be written as 1 + 4*a*a-2*a-2*a.
1 - 2*a + 4*a*a - 2*a.

Taking 1 as common in first two and 2*a in last two then 1(1 - 2*a)-2*a(1 - 2*a).
Hence (1 - 2*a)(1 - 2*a).

So Both Are Correct. So we have to choose any one of these such it satisfies the options available.

Varsha jadhav said:   6 years ago
@All.

We can take positive or negative square root that is (2a-1) or -(2a-1) => (1-2a) but according to the given option we need a positive value if we consider the value (2a-1) then the answer will be negative.

=> (2a-1)+3a.
=> 5a-1,
=>5*0.1039-1,
=>0.5195-1,
=>-0.4855.

but if we put the value (1-2a) then the calculation will be;
=>(1-2a)+3a.
=>1+a,
=>1+0.1039,
=>1.1039.
(2)

Harshit said:   8 years ago
Given that a = 0.1039; a<<1; this implies a^2<<<1 and hence it can be ignored int the expression.
So, the value should be approximately equal to 1 - a = 0.8961. The exact value is 0.9393 is also nearly equal to it.

But the option does not contain any matching value. So why should not we consider this question ambiguous?

Jaju said:   8 years ago
Hi @Bhavuk Singh.

How told you to take the square root of - .7922?

Actually, when you take the square root of (2a-1) ^2 it will give you two result either 2a-1 else 1-2a.

You can choose any of the two and yes, two results are possible here. Keeping in mind options given you have to select any one of twos. I think this is clear now?

G Anirudh said:   7 years ago

Here the given question can have 2 different answers as;

(1-2a)^2 = 4a^2-4a+1= (2a-1)^2.

Hence for questions like these, try to verify with both the answers and select the given option.
here answers are -0.4805 and 1.1039. so since all options are +ve we select the +ve ans i.e. 1.1039.

Iegarry@gmail.com said:   10 years ago
Let me explain this. When you solve the the equation under the square root, you can have either (2a - 1) or (1 - 2a). According to the question a = 0.1039.

Hence,
2a-1 = 2* 0.1039 -1 which would be negative. You cannot have a negative number inside the square root though.

Hence we have 1 - 2a.

4 = 2^2 and also 4=(-2)^2.
So sqrt 4 = 2, -2.

So sqrt 4a^2 -4a +1 = +(2a-1),-(2a-1).

So we have choose any one of these such it satisfies the options available.

+(2a-1) + 3a = 5a-1 = -1.5195 such option is not available.

-(2a-1) + 3a = a+1 = 1.1039 this one is option C.

Sq root of 4 is (+ or -) 2.

Because when we do (+ or - 2)^2 in both cases its +4.

Similarly +(1 - 2a)^2 is true and as well as -(1 - 2a)^2 i.e. (2a-1)^2 is also true.

How ever the answer in two cases are different.

So there must be an other answer except option C.

Uyog said:   3 years ago
Guys..this will make you understand,
Its 4a^2 * 4a+1... i.e a * 2ab+b^2.where a=2a...(4a^2) and b=1...
So, we got formula of (a-b)^2..removing root..i.e (a-b).

We get,
(2a-1)+3.
(2 * 0.1039- 1) + 3(0.1039).
(0.2078-1) + 0.3117.
0.7922 + 0.31 17.
1.1039.
(2)